Answer:
y = - [tex]\frac{1}{2}[/tex] x + 8
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 2x + 1 ← is in slope- intercept form
with slope m = 2
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{2}[/tex] , then
y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation
To find c substitute (4, 6 ) into the partial equation
6 = - 2 + c ⇒ c = 6 + 2 = 8
y = - [tex]\frac{1}{2}[/tex] x + 8 ← equation of perpendicular line
